design a circuit whose output will be high if the 4-bit data input value is greater than 9.

I have attempted to create a truth table and a Kmap, but will no luck.

 

What ideas do you have to begin?

 

If we label the bits B3, B2, B1, B0 it should be manifestly clear that there are six values greater than 9, namely 10, 11, 12, 13, 14, and 15

Each of them has B3 = 1. Equally clearly the value of B0 is a don't care -- that is it has no effect on the result. What we are left with is that either B2 or B1 or both must be equal to 1.

Thus:

GREATER_THAN_9 = B3 & (B2 | B1) ;

or in words B3 .AND. (B2 .OR. B1) ;

Can ya draw the K-map now?

 

All the 4 bit combinations above 9 should give a one on the truth table. Use SOP or POS to derive the boolean equation and then the logic circuit.

If you want you can use a simple DAC with 4 resistors and a comparator to sense the desired value.